1. Field of the Invention
The present invention is related to the field of servicing wellbores with electric wireline tools. More specifically, the present invention is related to the use of acoustic pulse-echo imaging tools, which are commonly run on electric wireline or cable in wellbores in an openhole, or portion of the wellbore which is not equipped with protective pipe or casing. Acoustic pulse-echo imaging tools are commonly run in the open-hole for constructing a graphic representation of acoustic reflection properties, and acoustic travel times from the tool exterior to the wellbore wall. The graphic representation approximates a visual image of the wellbore wall.
2. Description of the Related Art
Acoustic pulse-echo imaging tools are known in the art For example, "The Digital Circumferential Borehole Imaging Log--CBIL" Atlas Wireline Services, Houston, Tex. 1993, describes an acoustic pulse-echo imaging tool in detail. The acoustic pulse-echo imaging tool usually comprises a rotating head on which is mounted a piezoelectric element transducer. The transducer periodically emits an acoustic energy pulse on command from a controller circuit in the tool. After emission of the acoustic energy pulse, the transducer can be connected to a receiving circuit, generally located in the tool, for measuring a returning echo of the previously emitted acoustic pulse which is reflected off the wellbore wall. Circuitry, which can be in the tool or at the earth's surface measures the echo or reflection travel time and the reflection amplitude. The measurements of reflection time and reflection amplitude are used by circuitry at the earth's surface to generate a graph which corresponds to the visual appearance of the wellbore wall. The graph is used, for example, to measure the attitude of sedimentary features and to locate breaks or fractures in some earth formations.
Another application for electric wireline tools is measurement of the thickness of the casing. Casing, which is usually composed of steel alloy, is installed on at least a portion of most wellbores and is most commonly used for hydraulically isolating an earth formation that could be damaged or contaminated by fluids which may be produced from a different earth formation penetrated by the wellbore. Periodic measurement of the thickness of the casing is desirable for helping to determine the hydraulic integrity of the casing. Electric wireline tools are frequently used for measurement of casing thickness since the casing generally cannot be removed from the wellbore after the casing is installed. The most common types of wireline tools used for measurement of casing thickness are electromagnetic devices known as electromagnetic casing inspection tools "Casing Inspection Services", Atlas Wireline Services, Houston, Tex., 1991, describes some of the wireline tools used for casing thickness measurements. These tools generally work by passing a low frequency, usually 5-100 Hz, alternating current through a transmitter coil inside the inspection tool, and measuring, with a receiver coil also located inside the inspection tool, at least one property of the induced electromagnetic field in the casing.
Electromagnetic casing inspection tools are not very accurate for determining the absolute thickness of the casing because the casing inspection tool readings can be affected by such things as minute differences in metal composition which occur as a result of different manufacturing processes. Obtaining high accuracy measurements of casing thickness with electromagnetic casing inspection tools usually requires calibrating the electromagnetic casing inspection tool readings with a portion of known thickness of the casing being inspected. The calibration can be accomplished by first measuring the casing thickness prior to installation of the casing, with a device such as a caliper, and then performing a first run of the electromagnetic casing inspection tool immediately after installation of the casing. Calibration of measurements from an electromagnetic casing inspection tool can be difficult and expensive.
If the casing is composed of a material which does not have appropriate electrical and magnetic properties, then electromagnetic casing inspection tools cannot be used at all. For example, fiberglass reinforced plastic is used for the casing on certain wellbores adapted for solution mining. Determining casing thickness on wellbores with fiberglass reinforced plastic casing is not possible with electromagnetic casing inspection tools.
It is also known in the art to use measurements from acoustic pulse-echo imaging tools to derive the thickness of the casing. "Schlumberger Ultrasonic Borehole Imager--UBI" Schlumberger Limited, New York, 1992, describes a method of processing the reflections from an acoustic pulse-echo imaging tool to derive casing thickness. The method known in the art uses a Fast Fourier Transform (FFT) to analyze the frequency content of the acoustic energy in the reflection. Frequency content information is further analyzed to determine casing thickness. A time-varying electrical voltage is generated by the transducer in the tool as a result of the reflection. The time-varying electrical voltage is digitized in the tool to generate a first plurality of numbers, each number representing acoustic amplitude sampled at spaced-apart time intervals. The FFT processes the first plurality of numbers into a first plurality of number pairs representing amplitude as a function of frequency, and a second plurality of number pairs representing phase as a function of frequency. The method known in the art determines the resonant frequency of the casing, which is related to casing thickness, by calculating a first derivative function of the second plurality of number pairs representing phase as a function of frequency, and locating a frequency number at which a peak value of the first derivative function occurs. The method known in the art is difficult because the phase has a range of values of zero degrees to 360 degrees. If the phase values in the second plurality of number pairs reach either zero or 360 degrees, the phase values "wrap" or cross over to the other end of the phase value scale. For example, continuing from 359 degrees with a change in phase of 5 degrees per sample would provide a set of values which includes: 359, 4, 9, 14, etc. A graphic representation of the phase values resulting from a typical FFT would generally show a "saw-tooth" pattern because of the large number of crossovers that usually exists in a phase spectrum. Calculation of the first derivative function requires an additional processing step to "unwrap" the phase values into a nominally monotonic series of number pairs, whereby the crossover events are eliminated as a result of the unwrapping process. The unwrapping function is subject to significant error if the phase values do not trace a substantially smooth curve, particularly in the range of values near any of the crossovers.
It is an object of the present invention to provide a method for determining the thickness of a casing installed in a wellbore by using an acoustic pulse-echo imaging tool to derive the resonant frequency of the casing, wherein the first derivative function of the series of number pairs is calculated by an analytical process which does not require the step of unwrapping the phase values.